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STATISTICS RESEARCH – PROFESSOR DAVID ALDOUS GRAPHS Simulations of the I-Pod Process Max Moacanin 11/2012 The following pages contain graphs charting a number of different metrics concerning simulations of the I-Pod Process. The metrics include the popularity of the five most popularity songs (measured by how many users consider it to their favorite), the popularity of the most popular song as measured by the value it is given by the user, and the number of unique favorite songs. All of these metrics are graphed over standardized time.
Transcript of GRAPHS - University of California, Berkeley › ~aldous › Research › ...popularity of the five...
STATISTICS RESEARCH – PROFESSOR DAVID ALDOUS
GRAPHS Simulations of the I-Pod Process
Max Moacanin
11/2012
The following pages contain graphs charting a number of different metrics concerning simulations of the I-Pod Process. The metrics include the popularity of the five most popularity songs (measured by how many users consider it to their favorite), the popularity of the most popular song as measured by the value it is given by the user, and the number of unique favorite songs. All of these metrics are graphed over standardized time.
Top 5 Songs
The following graphs chart the popularity of the five most popular songs as measured by the number of users who consider it
to be their favorite song, i.e. the five songs with the highest values in the probability distribution of each user. There are graphs for
each of the three simulations conducted for the following parameters:
100 users, 50 songs, eta=0.03
500 users, 400 songs, eta=0.03
100 users, 50 songs, eta=0.015
500 users, 400 songs, eta=0.015
250 users, 100 songs, eta=0.03
250 users, 100 songs, eta=0.015
100 users, 50 songs, eta=0.0075
500 users, 400 songs, eta=0.0075
250 users, 100 songs, eta=0.0075
100 users, 50 songs, eta = 0.03
Simulation 1 Simulation 2 Simulation 3
500 users, 400 songs, eta = 0.03
Simulation 1 Simulation 2 Simulation 3
100 users, 50 songs, eta = 0.015
Simulation 1 Simulation 2 Simulation 3
500 users, 400 songs, eta = 0.015
Simulation 1 Simulation 2 Simulation 3
250 users, 100 songs, eta = 0.03
Simulation 1 Simulation 2 Simulation 3
250 users, 100 songs, eta = 0.015
Simulation 1 Simulation 2 Simulation 3
100 users, 50 songs, eta = 0.0075
Simulation 1 Simulation 2 Simulation 3
250 users, 100 songs, eta = 0.0075
Simulation 1 Simulation 2 Simulation 3
500 users, 400 songs, eta = 0.0075
Simulation 1 Simulation 2 Simulation 3
The Popularity of the Most Popular Song
The following graphs plot the popularity of the most popular song over standardized time. A song’s “popularity” is measured
by its probability of selection. The plots reflect simulations of 500 users with 50, 100, 200, and 400 songs. The four variations in the
number of songs are each represented in a single graph and distinguished by different colors.
500 users, eta=0.03
Normal Zoomed In
500 users, eta=0.015
Normal Zoomed In
500 users, eta=0.0075
Normal Zoomed In
Number of Unique Favorite Songs
The following graphs plot the number of unique favorite songs amongst 500 users over standardized time. The graphs plot data
for simulations with 50 songs, 100 songs, 200 songs, and 400 songs.
500 users, eta=0.03
Normal Zoomed In
500 users, eta=0.015
Normal Zoomed In
500 users, eta=0.0075
Normal Zoomed In
